

A134191


Impure numbers in the Collatz (3x+1) iteration.


2



2, 4, 5, 8, 10, 11, 13, 14, 16, 17, 20, 22, 23, 26, 28, 29, 31, 32, 34, 35, 38, 40, 41, 44, 46, 47, 49, 50, 52, 53, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 74, 76, 77, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 98, 100, 101, 103, 104, 106, 107, 110, 112, 113, 116, 118
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OFFSET

1,1


COMMENTS

Let f(k) be the trajectory of the Collatz iteration of the number k. Then Shaw calls a number n impure if n is in f(k) for some k < n. Shaw has an algorithm for finding congruences that the impure numbers satisfy.


LINKS

T. D. Noe, Table of n, a(n) for n=1..10000
Douglas J. Shaw, The Pure Numbers Generated by the Collatz Sequence, The Fibonacci Quarterly, Vol. 44, Number 3, August 2006, pp. 194201.


FORMULA

Complement of A061641.


EXAMPLE

The Collatz trajectory of 3 is (3,10,5,16,8,4,2,1), showing that the numbers 4,5,8,10,16 are impure.


MATHEMATICA

c[n_] := If[EvenQ[n], n/2, 3n + 1]; nn=1000; t=Table[0, {nn}]; Do[If[t[[n]]==0, m=n; While[m=c[m]; If[nn>=m>n && t[[m]]==0, t[[m]]=n]; m>nn  t[[m]]>0]], {n, nn}]; Flatten[Position[t, _?(#>0&)]]


CROSSREFS

Sequence in context: A094591 A189093 A325442 * A286803 A026138 A026170
Adjacent sequences: A134188 A134189 A134190 * A134192 A134193 A134194


KEYWORD

nonn


AUTHOR

T. D. Noe, Oct 12 2007


STATUS

approved



